Multi-mode spiral delay device

ABSTRACT

An optical device includes a first multi-mode waveguide, a first optical coupler coupled to the first multi-mode waveguide, the first coupler being tapered and curved, and a first single-mode waveguide having a first end coupled to the first optical coupler. The optical device maybe used in an optical delay device. A method of propagating light in a first multi-mode waveguide toward a first optical coupler, propagating the light in the first optical coupler toward a first single-mode waveguide, the first optical coupler being tapered and curved, and propagating the light along the first single-mode waveguide is also disclosed.

RELATED APPLICATIONS

This application claims the benefit of, and priority to, U.S.Provisional Application No. 62/848,473, filed May 15, 2019, entitled“Multi-Mode Spiral Delay Device,” which is incorporated by referenceherein in its entirety.

TECHNICAL FIELD

This relates generally to photonic devices and, more specifically, tooptical delay devices.

BACKGROUND

Optical waveguides (or waveguides) are widely used for transmittinglight. For example, optical fibers are used in various telecommunicationsystems. Slab or planar waveguides are used in photonic devices formanipulating light (such as directing light, coupling light, filteringlight, generating light output, etc.).

Optical delay devices used in various optical applications, such astime-resolved spectroscopy, interferometry, and time divisional opticalcommunications often include optical waveguides. In order to provide asufficient delay, optical delay devices would include long opticalwaveguides, which increase the overall size of the optical delaydevices. Accordingly, there is a need for an optical delay device havinga compact size.

SUMMARY

One or more embodiments of the present disclosure provide an opticaldelay device that includes a first multi-mode waveguide spiraling inwardtoward a center region of the optical delay device, and a first couplerthat is coupled to the first multi-mode waveguide and configured toreceive light from the first multi-mode waveguide. The first couplerspirals further inward towards a center region of the optical delaydevice. The optical delay device also includes a first single-modewaveguide that is located in the center region and configured to receivelight from the first coupler, and a second coupler configured to receivelight from the first single-mode waveguide, the second coupler spiralingoutward from the center region. The optical device further includes asecond multi-mode waveguide that is coupled to the second coupler andconfigured to receive light from the second coupler. The second couplerspirals further outward from the center region. A first end of the firstsingle-mode waveguide is coupled to the first coupler and a second endof the first single-mode waveguide, opposite to the first end, iscoupled to the second coupler.

In some embodiments, the first multi-mode waveguide includes a firstplurality of spiral rounds. The first plurality of spiral roundsincludes a first outmost spiral portion that has a first radius ofcurvature and a first inmost spiral portion that has a second radius ofcurvature that is smaller than the first radius of curvature. Spiralportions between the first outmost spiral portion and the first inmostspiral portion have successively decreasing radii from the first radiusof curvature to the second radius of curvature. The first couplerincludes a second plurality of spiral rounds. The second plurality ofspiral rounds includes a second outmost spiral portion that has a thirdradius of curvature and a second inmost spiral portion that has a fourthradius of curvature that is smaller than the third radius of curvature.Spiral portions between the second outmost spiral portion and the secondinmost spiral portion have successively decreasing radii from the thirdradius of curvature to the fourth radius of curvature. The secondcoupler includes a third plurality of spiral rounds. The third pluralityof spiral rounds includes a third inmost spiral portion that has a fifthradius of curvature and a third outmost spiral portion that has a sixthradius of curvature that is larger than the fifth radius of curvature.Spiral portions between the third inmost spiral portion and the thirdoutmost spiral portion have successively increasing radii from the fifthradius of curvature to the sixth radius of curvature. The secondmulti-mode waveguide includes a fourth plurality of spiral rounds. Thefourth plurality of spiral rounds includes a fourth inmost spiralportion that has a seventh radius of curvature and a fourth outmostspiral portion that has an eighth radius of curvature that is largerthan the seventh radius of curvature. Spiral portions between the fourthinmost spiral portion and the fourth outmost spiral portion havesuccessively increasing radii between the seventh radius of curvatureand the eighth radius of curvature.

In some embodiments, the first single-mode waveguide includes a curvedportion having a radius of curvature that is smaller than each of thefourth radius of curvature and the fifth radius of curvature.

In some embodiments, the first plurality of spiral rounds is interleavedwith the fourth plurality of spiral rounds and the second plurality ofspiral rounds is interleaved with the third plurality of spiral rounds.Any portion of the first plurality of spiral rounds is separated fromany adjacent portion of the fourth plurality of spiral rounds forpreventing light propagating in the first plurality of spiral roundsfrom being evanescently coupled into the fourth plurality of spiralrounds. Any portion of the second plurality of spiral rounds isseparated from any adjacent portion of the third plurality of spiralrounds for preventing light propagating in the second plurality ofspiral rounds from being evanescently coupled into the third pluralityof spiral rounds.

In some embodiments, the first plurality of spiral rounds has a firstnumber of spiral rounds, the second plurality of spiral rounds has asecond number of spiral rounds, the third plurality of spiral rounds hasa third number of spiral rounds that corresponds to the second number ofspiral rounds, and the fourth plurality of spiral rounds has a fourthnumber of spiral rounds that corresponds to the first number of spiralrounds.

In some embodiments, the optical delay device includes at least 10spiral rounds (e.g., a total number of spiral rounds in the firstplurality of spiral rounds, the second plurality of spiral rounds, thethird plurality of spiral rounds, and the fourth plurality of spiralrounds is at least 10). In some embodiments, the optical delay deviceincludes at least 100 spiral rounds (e.g., the total number of spiralrounds in the first plurality of spiral rounds, the second plurality ofspiral rounds, the third plurality of spiral rounds, and the fourthplurality of spiral rounds is at least 100).

In some embodiments, the eighth radius of curvature is substantiallyequal to the first radius of curvature, the seventh radius of curvatureis substantially equal to the second radius of curvature, the sixthradius of curvature is substantially equal the third radius ofcurvature, the fifth radius of curvature is substantially equal thefourth radius of curvature, the third radius of curvature issubstantially equal to the second radius of curvature, and the seventhradius of curvature is substantially equal to the sixth radius ofcurvature.

In some embodiments, the first plurality of spiral rounds, the secondplurality of spiral rounds, the third plurality of spiral rounds, andthe fourth plurality of spiral rounds are concentric spiral rounds.

In some embodiments, the optical delay device also includes an inputcoupler that is adiabatically coupled to the first multi-mode waveguideand an output coupler that is adiabatically coupled to the secondmulti-mode waveguide. The first multi-mode waveguide is configured toreceive light from the input coupler and propagate the light toward tofirst coupler. The second multi-mode waveguide is configured topropagate light received from the second coupler toward the outputcoupler.

In some embodiments, the input coupler includes a portion having thefirst radius of curvature and the output coupler includes a portionhaving the eighth radius of curvature.

In some embodiments, the first multi-mode waveguide has a first width,the second multi-mode waveguide has a second width, and the firstsingle-mode waveguide has a third width that is smaller than each of thefirst width and the second width. The first coupler has a width thattapers from the first width to the third width and the second couplerhas a width that tapers from the second width to the third width.

In some embodiments, the first multi-mode waveguide has a first length,the second multi-mode waveguide has a second length, and the firstsingle-mode waveguide has a third length; that is smaller than each ofthe first length and the second length.

In some embodiments, the first multi-mode waveguide, the secondmulti-mode waveguide, the first single-mode waveguide, the firstcoupler, and the second coupler are formed in a same layer of a materialon a substrate.

One or more embodiments of the present disclosure provide a method ofpropagating light, the method includes receiving light, propagating thelight in a first multi-mode waveguide toward a first coupler, andpropagating the light in the first coupler toward a first single-modewaveguide such that the first multi-mode waveguide and the first couplerprovide a first light path that spirals inward toward a center region.The method also includes propagating the light along the firstsingle-mode waveguide toward a second coupler, propagating the light inthe second coupler toward a second multi-mode waveguide, propagating thelight in the second multi-mode waveguide, and outputting the light. Thesecond coupler and the second multi-mode waveguide provide a secondlight path that spirals outward from the center region. The firstsingle-mode waveguide provides a third light path through the centerregion and between the first light path and the second light path.

In some embodiments, the first light path includes a first plurality ofspiral rounds corresponding to the first multi-mode waveguide. The firstplurality of spiral rounds includes a first outmost spiral portion thathas a first radius of curvature and a first inmost spiral portion thathas a second radius of curvature that is smaller than the first radiusof curvature. Spiral portions between the first outmost spiral portionand the first inmost spiral portion have successively decreasing radiifrom the first radius of curvature to the second radius of curvature.The first light path also includes a second plurality of spiral roundscorresponding to the first coupler. The second plurality of spiralrounds includes a second outmost spiral portion that has a third radiusof curvature and a second inmost spiral portion that has a fourth radiusof curvature that is smaller than the third radius of curvature. Spiralportions between the second outmost spiral portion and the second inmostspiral portion have successively decreasing radii from the third radiusof curvature to the fourth radius of curvature. The second light pathincludes a third plurality of spiral rounds corresponding to the secondcoupler. The third plurality of spiral rounds includes a third inmostspiral portion that has a fifth radius of curvature and a third outmostspiral portion that has a sixth radius of curvature that is larger thanthe fifth radius of curvature. Spiral portions between the third inmostspiral portion and the third outmost spiral portion have successivelyincreasing radii from the fifth radius of curvature to the sixth radiusof curvature. The second light path further includes a fourth pluralityof spiral rounds corresponding to the second multi-mode waveguide. Thefourth plurality of spiral rounds includes a fourth inmost spiralportion that has a seventh radius of curvature and a fourth outmostspiral portion that has an eighth radius of curvature that is largerthan the seventh radius of curvature. Spiral portions between the fourthinmost spiral portion and the fourth outmost spiral portion havesuccessively increasing radii from the seventh radius of curvature tothe eighth radius of curvature.

In some embodiments, propagating the light along the first single-modewaveguide includes propagating the light along a curved path having aradius of curvature that is smaller than each of the fourth radius ofcurvature and the fifth radius of curvature.

In some embodiments, the first plurality of spiral rounds has a firstnumber of spiral rounds, the second plurality of spiral rounds has asecond number of spiral rounds, the third plurality of spiral rounds hasa third number of spiral rounds that corresponds to the second number ofspiral rounds, and the fourth plurality of spiral rounds has a fourthnumber of spiral rounds that corresponds to the first number of spiralrounds.

In some embodiments, receiving the light includes propagating the lightalong an input single-mode waveguide toward an input coupler andpropagating the light along the input coupler toward the firstmulti-mode waveguide. In some embodiments, outputting the light includescoupling the light from the second multi-mode waveguide, through anoutput coupler, to an output single-mode waveguide and propagating thelight along the output single-mode waveguide.

In some embodiments, propagating the light along the input couplerincludes propagating the light along a path that has the first radius ofcurvature. In some embodiments, coupling the light from the secondmulti-mode waveguide, through the output coupler, to the outputsingle-mode waveguide includes propagating the light along a path havingthe eighth radius of curvature.

In some embodiments, propagating the light in the first multi-modewaveguide also includes propagating the light along the first multi-modewaveguide without evanescently coupling the light into the secondmulti-mode waveguide, propagating the light in the first couplerincludes propagating the light along the first coupler withoutevanescently coupling the light into the second coupler, propagating thelight in the second coupler also includes propagating the light alongthe second coupler without evanescently coupling the light into thefirst coupler, and propagating the light in the second multi-modewaveguide includes propagating the light along the second multi-modewaveguide without evanescently coupling the light into the firstmulti-mode waveguide.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the various described embodiments,reference should be made to the Detailed Description below, inconjunction with the following drawings in which like reference numeralsrefer to corresponding parts throughout the figures.

FIG. 1A is a simplified diagram illustrating an optical delay device andan optical path of light propagating through different portions of theoptical delay device in accordance with some embodiments.

FIGS. 1B-1D are plan views of an optical delay device in accordance withsome embodiments.

FIG. 1E is a partial plan view of an optical delay device illustrating acenter region of the optical device shown in FIGS. 1A-1D in accordancewith some embodiments.

FIG. 1F is a linearized view of the optical delay device shown in FIGS.1A-1D in accordance with some embodiments.

FIG. 1G is a cross-sectional view of the optical delay device shown inFIGS. 1A-1D in accordance with some embodiments.

FIG. 2A is a simplified diagram illustrating an optical delay device andan optical path of light propagating through different portions of theoptical delay device in accordance with some embodiments.

FIGS. 2B-2C are plan views of an optical delay device in accordance withsome embodiments.

FIG. 2D is a partial plan view of an optical delay device illustratingan input region of the optical device shown in FIGS. 2A-C in accordancewith some embodiments.

FIG. 2E is a linearized view of the optical delay device shown in FIGS.2A-2C in accordance with some embodiments.

FIGS. 3A-3C are flowcharts illustrating a method of propagating light tocreate an optical delay in accordance with some embodiments.

Like reference numerals refer to corresponding parts throughout theseveral views of the drawings. The drawings may not be drawn to scaleunless stated otherwise.

DETAILED DESCRIPTION

As explained above, there is a need for an optical delay device (orphotonic delay line) that is compact. The disclosed optical delaydevices and methods described herein meet the need by allowingtransmission of light in a spiral optical path with a small footprint ona substrate. A majority of the delay path of the optical delay devicesinclude multi-mode waveguides, resulting in reduced optical loss aslight propagates along the optical delay device.

Reference will now be made in detail to embodiments, examples of whichare illustrated in the accompanying drawings. In the following detaileddescription, numerous specific details are set forth in order to providea thorough understanding of the various described embodiments. However,it will be apparent to one of ordinary skill in the art that the variousdescribed embodiments may be practiced without these specific details.In other instances, well-known methods, procedures, components,circuits, and networks have not been described in detail so as not tounnecessarily obscure aspects of the embodiments.

It will also be understood that, although the terms first, second, etc.are, in some instances, used herein to describe various elements, theseelements should not be limited by these terms. These terms are used onlyto distinguish one element from another. For example, a first waveguidecould be termed a second waveguide, and, similarly, a second waveguidecould be termed a first waveguide, without departing from the scope ofthe various described embodiments. The first waveguide and the secondwaveguide are both waveguides, but they are not the same waveguide.

FIG. 1A is a simplified diagram illustrating an optical delay device 100and an optical path of light propagating in the optical delay device inaccordance with some embodiments. As shown, optical delay device 100includes a first multi-mode waveguide 106-in providing a first portionof the optical path that spirals inward toward a center region 102 ofoptical delay device 100. First multi-mode waveguide 106-in is coupled(e.g., physically, optically) to a first coupler 104-in, which providesa second portion of the optical path that spirals further inward towardcenter region 102 of optical delay device 100. Optical delay device 100further includes a first single-mode waveguide 102-A disposed (e.g.,located) in center region 102 and providing a third portion of theoptical path through the center region. Optical delay device 100 alsoincludes a second coupler 104-out providing a fourth portion of theoptical path that spirals outward from center region 102. Second coupler104-out is coupled (e.g., physically, optically) to a second multi-modewaveguide 106-out, which provides a fifth portion of the optical paththat spirals further outward from center region 102. First single-modewaveguide 102-A has a first end and a second end that is opposite to thefirst end. The first end of first single-mode waveguide 102-A is coupled(e.g., physically, optically) to first coupler 104-in and the second endof first single-mode waveguide 102-A is coupled (e.g., physically,optically) to second coupler 104-out. Lines with upward pointing arrowscorrespond to waveguides that spiral inward towards center region 102(e.g., first multi-mode waveguide 106-in and first coupler 104-in) andlines with downward pointing arrows correspond to waveguides that spiraloutwards from center region 102 (e.g., second multi-mode waveguide106-out and second coupler 104-out).

First single-mode waveguide 102-A is configured to allow propagation oflight in a fundamental optical mode (e.g., TE₀). For example, firstsingle-mode waveguide may have a width of 1 micrometer or less.Typically, propagation of light in higher order modes (e.g., opticalmodes that are not the fundamental optical mode, such as TE₁, TE₂, etc.)is prohibited in single-mode waveguides. In contrast, multi-modewaveguide 106-in or 106-out is configured to allow light to propagate,along the multi-mode waveguide, in one or more of a plurality of modesincluding the fundamental optical mode and higher order modes (e.g.,light in a higher order mode as well as light in the fundamental opticalmode can propagate through the multi-mode waveguide). For example,multi-mode waveguide 106-in or 106-out may have a width that is greaterthan 1 micrometer. In general, for propagation of light having aparticular wavelength, a single-mode waveguide has a smaller widthcompared to a multi-mode waveguide.

First multi-mode waveguide 106-in is configured to receive light, and topropagate the light along an inward spiral toward first coupler 104-in.First coupler 104-in is configured to receive the light from the firstmulti-mode waveguide, and to adiabatically couple the light to firstsingle-mode waveguide 102-A, which is configured to transmit the lighttoward second coupler 104-out while changing the propagation directionof the light. Second coupler is configured to receive the light fromfirst single-mode waveguide and to adiabatically couple the light tosecond multi-mode waveguide 106-out, which is configured to propagatethe light along an outward spiral to an output of optical delay device100. Arrows shown along the waveguides of optical delay device 100indicate the optical path (e.g., propagation direction, traveldirection) of light in optical delay device 100.

FIGS. 1B-1D are plan views of optical delay device 100 in accordancewith some embodiments. As shown in FIG. 1B, first multi-mode waveguide106-in can be coupled to an input multi-mode waveguide 190-in at aninput 191 of optical delay device 100, and second multi-mode waveguide106-out can be coupled to an output multi-mode waveguide 190-out at anoutput 192 of optical delay device 100. As shown, optical delay device100 is configured to receive light 199 at input 191 and to propagatelight 199 through first multi-mode waveguide 106-in and first coupler104-in in inward spirals toward center region 102, through firstsingle-mode waveguide 102-A in the center region, and then throughsecond coupler 104-out and second multi-mode waveguide 106-out inoutward spirals toward output 192. FIG. 1B also shows inset A, which isa zoomed-in view of a portion 106 b of a second annular region 106 nearinput 191. Lines with downward pointing arrows correspond to firstmulti-mode waveguide 106-in and lines with upward pointing arrowscorrespond to second multi-mode waveguide 106-out.

FIG. 1C shows input 191 having a distance R1 from a center 101 ofoptical delay device 100, and output 192 having a distance R2 fromcenter 101 of optical delay device 100. In some embodiments, R2 is equalto R1 (or differing by less than 1%). FIG. 1C also indicates a junction193, at which the inward spirals of optical delay device 100 transitionfrom first multi-mode waveguide 106-in to first coupler 104-in, or atwhich first multi-mode waveguide 106-in is coupled to first coupler104-in. Junction 193 has a distance R3 from center 101. FIG. 1C alsoindicates a junction 194, at which the outward spirals of optical delaydevice 100 transition from second coupler 104-out to second multi-modewaveguide 106-out, or at which second multi-mode waveguide 106-out iscoupled to second coupler 104-out. Junction 194 has a distance R4 fromcenter 101. In some embodiments, R4 is equal to R3 (or differing by lessthan 1%). FIG. 1C also indicates a junction 195, at which the inwardspirals of optical delay device 100 transition from first coupler 104-into first single-mode waveguide 102-A, or at which first coupler 104-inis coupled to first single-mode waveguide 102-A. Junction 195 has adistance R5 from center 101. FIG. 1C also indicates a junction 196, atwhich the outward spirals of optical delay device 100 transition fromfirst single-mode waveguide 102-A to second coupler 104-out, or at whichsecond coupler 104-out is coupled to first single-mode waveguide 102-A.Junction 196 has a distance R6 from center 101. In some embodiments, R6is equal to R5 (or differing by less than 1%).

As shown in FIG. 1C, first multi-mode waveguide 106-in includes a firstplurality of spiral rounds located between a first outmost spiralportion 112-1 and a first inmost spiral portion 112-2 of firstmulti-mode waveguide 106-in (e.g., spiral rounds located in secondannular region 106 and corresponding to first multi-mode waveguide106-in). The first outmost spiral portion 112-1 has a first radius ofcurvature that corresponds to distance R1. The first inmost spiralportion 112-2 has a second radius of curvature that corresponds todistance R3 and is smaller than the first radius of curvature. Spiralportions that are located between the first outmost spiral portion 112-1and the first inmost spiral portion 112-2 have successively decreasingradii that decrease continuously and monotonously from R1 to R3.

As shown in FIG. 1C, first coupler 104-in includes a second plurality ofspiral rounds located between a second outmost spiral portion 112-3 anda second inmost spiral portion 112-4 of first coupler 104-in (e.g.,spiral rounds located in first annular region 104, shown in inset B ofFIG. 1E as spiral rounds with decreasing widths). The second outmostspiral portion 112-3 has a third radius of curvature that corresponds todistance R3. The second inmost spiral portion 112-4 has a fourth radiusof curvature that corresponds to distance R5 and is smaller than thethird radius of curvature. Spiral portions that are located between thesecond outmost spiral portion 112-3 and the second inmost spiral portion112-4 have successively decreasing radii that decrease continuously andmonotonously from R3 to R5. In some embodiments, the second radius ofcurvature and the third radius of curvature both correspond to distanceR3.

As shown in FIG. 1C, second coupler 104-out includes a third pluralityof spiral rounds located between a third inmost spiral portion 112-5 anda third outmost spiral portion 112-6. The third inmost spiral portion112-5 has a fifth radius of curvature corresponding to distance R6. Thethird outmost spiral portion 112-6 has a sixth radius of curvaturecorresponding to distance R4 and is larger than the fifth radius ofcurvature. Spiral portions that are located between the third inmostspiral portion 112-5 and the third outmost spiral portion 112-6 havesuccessively increasing radii that increase continuously andmonotonously from R6 to R4. In some embodiments, the third radius ofcurvature of the second outmost spiral portion 112-3 and the sixthradius of curvature of the third outmost spiral portion 112-6 bothcorrespond to distance R3. In some embodiments, the fourth radius ofcurvature of the second inmost spiral portion 112-4 and the fifth radiusof curvature of the third inmost spiral portion 112-5 both correspond todistance R5.

As shown in FIG. 1C, second multi-mode waveguide 160-out includes afourth plurality of spiral rounds located between a fourth inmost spiralportion 112-7 and a fourth outmost spiral portion 112-8 of secondmulti-mode waveguide 106-out (e.g., spiral rounds located in secondannular region 106 and corresponding to second multi-mode waveguide106-out). The fourth inmost spiral portion 112-7 has a seventh radius ofcurvature corresponding to distance R4. The fourth outmost spiralportion 112-8 has an eighth radius of curvature corresponding todistance R2 and is larger than the seventh radius of curvature. Spiralportions that are located between the fourth inmost spiral portion 112-7and the fourth outmost spiral portion 112-8 have successively increasingradii that increase continuously and monotonously between R4 and R2. Insome embodiments, the seventh radius of curvature does not correspond todistance R4 (e.g., the seventh radius of curvature may be greater thandistance R4).

First single-mode waveguide 102-A, shown in FIG. 1C, includes curvedportions having a radius of curvature that is smaller than R4 and R5.

In some embodiments, the first plurality of spiral rounds (correspondingto first multi-mode waveguide 106-in), the second plurality of spiralrounds (corresponding to first coupler 104-in), the third plurality ofspiral rounds (corresponding to second coupler 104-out), and the fourthplurality of spiral rounds (corresponding to second multi-mode waveguide106-out) are concentric spiral rounds.

As shown in FIG. 1D, optical delay device 100 includes center region 102where first single-mode waveguide 102-A shown in FIG. 1C is located.Optical delay device also includes a first annular region 104 between avirtual circle with a radius corresponding to distance R5 and a virtualcircle with a radius corresponding to distance R3 that surrounds centerregion 102, and a second annular region 106 between a virtual circlewith a radius corresponding to distance R3 and a virtual circle with aradius corresponding to distance R1 that surrounds first annular region104 and center region 102. First coupler 104-in or at least a portion(e.g., a majority portion, or more than 90 percent) of first coupler104-in are located within the first annular region 104. Likewise, secondcoupler 104-out or at least a portion (e.g., a majority portion, or morethan 90 percent) of second coupler 104-out are located within the firstannular region 104. First multi-mode waveguide 106-in, or at least aportion (e.g., a majority portion, or more than 90%) of first multi-modewaveguide 106-in are located within the second annular region 106.Likewise, second multi-mode waveguide 106-out, or at least a portion(e.g., a majority portion, more than half) of second multi-modewaveguide 106-out are located within the second annular region 106.

In some embodiments, center region 102 has a diameter that is between 10micrometers and 500 micrometers (i.e., 10 micrometers<R5<500micrometers). In some embodiments, center region 102 has a diameter thatis approximately 300 micrometers (i.e., R5˜300 micrometers). Once R5 isfixed, other dimensions (e.g., R3, R1) can be determined based onrequired lengths for the corresponding parts (e.g., first coupler104-in, and first multimode waveguide 106-in) of optical delay device100. For example, in certain embodiments, R5 is approximately 100micrometers, and R3 is approximately 130 micrometers. In anotherexample, R5 is approximately 10 micrometers, and R3 is approximately 100micrometers.

FIG. 1E provides a zoomed-in view of an area 104 c of optical delaydevice 100, corresponding to area 104 c of optical delay device 100shown in FIG. 1D. Area 104 c includes center region 102, first annularregion 104, and portions of second annular region 106 of optical delaydevice 100 in accordance with some embodiments. FIG. 1E also provides afurther zoomed view in inset B showing first coupler 104-in in firstannular region 104 having decreasing width as it spirals inward towardcenter region 102, and second coupler 104-out in first annular region104 having increasing width as it spirals outward from center region102.

FIG. 1F is a linearized (or stretched-out) view of optical delay device100 shown in FIGS. 1A-1D and illustrates the dimensions of variousportions of optical delay device 100. As shown in FIG. 1F, optical delaydevice 100 provides an optical path having an overall length of L forlight 199 propagating through:

-   -   first multi-mode waveguide 106-in;    -   first coupler 104-in;    -   first single-mode waveguide 102-A;    -   second coupler 104-out; and    -   second multi-mode waveguide 106-out.

As shown in FIG. 1F, first multi-mode waveguide 106-in has a firstlength L1, second multi-mode waveguide 106-out has a second length L2,and first single-mode waveguide 102-A has a third length L3 that is muchsmaller than each of the first length L1 and the second length L2 (i.e.,L3<<L1, L2). In some embodiments, the third length L3 depends ondistance R5 or R6. For example, in some embodiments, third length L3 isbetween two to four times distance R5. Since R5 can be between 10micrometers to 500 micrometers, third length L3 can be between 20micrometers and 2,000 micrometers. For example, in some embodiments, R5is 10 micrometers, L3 is between 30 micrometers and 40 micrometers. Inanother example, when R5 is 500 micrometers, L3 is between 1,500micrometers and 2000 micrometers. For example, in some embodiments,third length L3 is approximately 400 micrometers, and first length L1and second length L2 in combination can constitute a majority (e.g.,more than 90%) of the overall optical path length L, which can be in therange of tens of centimeters. In some embodiments, the first length L1and the second length L2 are substantially the same (e.g., differing byless than 1% or 0.001%).

In some embodiments, it is desirable for the first multi-mode waveguide160-in and the second multi-mode waveguide 160-out to constitute themajority of the waveguide length.

In some embodiments, first coupler 104-in has a fourth length L4 andsecond coupler 104-out has a fifth length L5. In some embodiments,fourth length L4 is less than first length L1, fifth length L5 is lessthan second length L2, and third length L3 is smaller than each offourth length L4 and fifth length L5 (i.e., L3<L4, L5). In someembodiments, fourth length L4 and fifth length L5 are substantially thesame (e.g., differing by less than 1% or 0.001%). In some embodiments,fourth length L4 and fifth length L5 are each greater than 1 millimeter.In some embodiments, fourth length L4 and fifth length L5 areapproximately 3 millimeters.

Equation 1 may be used to determine first length L1 of first multi-modewaveguide 160-in and second length L2 of second multi-mode waveguide160-out, assuming that the two multi-mode waveguides are equal inlength:

$\begin{matrix}{L_{1,2} = {\frac{L}{2} - L_{4,5} - \frac{L_{3}}{2}}} & (1)\end{matrix}$

In Equation 1, L_(1,2) is the first length L1 or second length L2, L isthe overall length, L_(4,5) is the fourth length L4 or fifth length L5,and L₃ is the third length L3.

For example, for an optical delay device that has an overall opticalpath length L of 40 centimeters (e.g., L=400 millimeters), a thirdlength L3 of 0.4 millimeters, a fourth length L4 of 3 millimeters, and afifth length L5 of 3 millimeters, each of the first length L1 and thesecond length L2 would be approximately 197 millimeters (e.g., L1,L2=19.7 centimeters). In another example, for an optical delay devicethat has an optical path length L of 80 centimeters (e.g., L=800millimeters) and all other lengths as described in the previous example,each of the first length L1 and the second length L2 would beapproximately 397 millimeters (e.g., L1, L2=39.7 centimeters). In someembodiments, the combined first length L1 of the first multi-modewaveguide 160-in and second length L2 of the second multi-mode waveguide160-out constitute at least 95% of the overall length of optical delaydevice (e.g., L1+L2≥95% L). Preferably, the combined first length L1 ofthe first multi-mode waveguide 160-in and second length L2 of the secondmulti-mode waveguide 160-out constitute at least 98% of the totalcombined waveguide length of optical delay device (e.g., L1+L2≥98% L).

As shown in FIG. 1F, first multi-mode waveguide 106-in has a first widthw1, second multi-mode waveguide 106-out has a second width w2, and firstsingle-mode waveguide 102-A has a third width w3 that is smaller thaneach of the first width w1 and the second width w2 (i.e., w3<w1, w2).First coupler 104-in has a width that tapers from the first width w1 tothe third width w3. Second coupler 140-out has a width that tapers fromthe third width w3 to the second width w2. In some embodiments, thefirst width w1 and the second width w2 are substantially the same (e.g.,w1˜w2, differing by less than 1%). In some embodiments, the first widthw1 and the second width w2 are between 3 micrometers and 4 micrometers(e.g., 3 micrometers≤w1, w2≤4 micrometers). In some embodiments, thefirst width w1 and the second width w2 are at least 3 micrometers (e.g.,w1, w2≥3 micrometers). In some embodiments, the first width w1 and thesecond width w2 are at least 1 micrometer (e.g., w1, w2≥1 micrometers).In some embodiments, the third width w3 is between 400 nanometers and500 nanometers (e.g., 400 nanometers<w3<500 nanometers). In someembodiments, the third width w3 is less than 1 micrometer (e.g., w3<1micrometers).

First coupler 104-in is configured to adiabatically couple light fromfirst multi-mode waveguide 106-in to first single-mode waveguide 102-A.Second coupler 104-out is configured to adiabatically couple light fromfirst single-mode waveguide 102-A to second multi-mode waveguide106-out. For example, one or more of first coupler 104-in and secondcoupler 104-out may have a linear taper profile, a parabolic taperprofile, or an exponential taper profile. For example, first coupler104-in or second coupler 104-out can have a length of at least 100micrometers, a largest tapering angle θ in first coupler 104-in orsecond coupler 104-out is less than 0.3 degrees.

FIG. 1G is a cross-sectional view of optical delay device 100 shown inFIGS. 1B-1D. Cross-sectional views of the first plurality of spiralrounds corresponding to first multi-mode waveguide 106-in, the secondplurality of spiral rounds corresponding to first coupler 104-in, thethird plurality of spiral rounds corresponding to second coupler104-out, the fourth plurality of spiral rounds corresponding to secondmulti-mode waveguide 106-out, and first single-mode waveguide 102-A areshown. FIG. 1G also includes insets illustrating top views of variousportions of optical delay device 100. In FIG. 1G, bonded shapes with alighter fill pattern correspond to portions of waveguides that areconfigured to transmit light toward first single-mode waveguide 102-A,i.e., the first plurality of spiral rounds (e.g., 106-in-1 to 106-in-n)and the second plurality of spiral rounds (e.g., 104-in-1 to 104-in-n)corresponding to first multi-mode waveguide 106-in and first coupler104-in, respectively. Likewise, bonded shapes with a darker fill patterncorrespond to portions of waveguides that are configured transmit lightaway from first single-mode waveguide 102-A, i.e., the third pluralityof spiral rounds (e.g., 104-out-1 to 104-out-n) and the fourth pluralityof spiral rounds (e.g., 106-out-1 to 106-out-n) corresponding to secondcoupler 104-out second multi-mode waveguide 106-out, respectively.Bonded shapes with no fill pattern correspond to the first single-modewaveguide 102-A.

Referring to inset C, which shows a top view of a portion of secondannular region 106, the first plurality of spiral rounds (e.g., 106-in-1to 106-in-n) is interleaved with the fourth plurality of spiral rounds(e.g., 106-out-1 to 106-out-n). Any portion of the first plurality ofspiral rounds is separated from any adjacent portion of the fourthplurality of spiral rounds by a distance d1, which is designed to belarge enough in order to prevent light propagating in the firstplurality of spiral rounds from being evanescently coupled into thefourth plurality of spiral rounds. As shown in inset C, waveguideportion 106-in-2, which is a portion of the first plurality of spiralrounds and has the first width w1, is located between waveguide portions106-out-1 and 106-out-2, which are portions of the fourth plurality ofspiral rounds and have the second width w2. A respective sidewall ofwaveguide portion 106-in-2 is spaced apart from a respective sidewall ofwaveguide portions 106-out-1 and 106-out-2 by distance d1. In someembodiments, distance d1 is greater than or equal to 1 micrometer (e.g.,d1≥1 micrometer). In some embodiments, distance d1 is greater than orequal to 2 micrometers (e.g., d1≥2 micrometers). In some embodiments,distance d1 is greater than or equal to 8 micrometers. Thus, any portionof the first plurality of spiral rounds is separated from any adjacentportion of the fourth plurality of spiral rounds by distance d1, whichis designed to be large enough in order to prevent light propagating inthe first plurality of spiral rounds from being evanescently coupledinto the fourth plurality of spiral rounds (or vice versa).

Referring to inset D, which shows a top view of a portion of firstannular region 104, the second plurality of spiral rounds (e.g.,104-in-1 to 104-in-n) is interleaved with the third plurality of spiralrounds (e.g., 104-out-1 to 104-out-n). Any portion of the secondplurality of spiral rounds is separated from any adjacent portion of thethird plurality of spiral rounds by distance d2, which is designed to belarge enough in order to prevent light propagating in the secondplurality of spiral rounds from being evanescently coupled into thethird plurality of spiral rounds (or vice versa). As shown in inset D,waveguide portion 104-in-2, which is a portion of the second pluralityof spiral rounds, is located adjacent to and between waveguide portions104-out-2 and 104-out-3, which are portions of the third plurality ofspiral rounds. Waveguide portion 104-out-2 has a fourth width w4 andwaveguide portion 104-out-3 has a fifth width w5 that is smaller thanfourth width w4. Fourth width w4 is smaller than second width w2 ofsecond multi-mode waveguide 106-out and fifth width w5 is larger thanthird width w3 of first single-mode waveguide 102-A (i.e., w2>w4>w5>w3).Waveguide portion 104-in-2 has a sixth width w6 a that is similar tofourth width w4 and a seventh width w7 that is substantially equal(e.g., similar) to fifth width w5. Sixth width w6 is smaller than firstwidth w1 of first multi-mode waveguide 106-in and seventh width w7 islarger than third width w3 of first single-mode waveguide 102-A. In someembodiments, width w6 is equal to or less than width w4 of waveguideportion 104-out-2 and width w7 is equal to or greater than width w5 ofwaveguide portion 104-out-3. A respective sidewall of waveguide portion104-in-2 is spaced apart from a respective sidewall of waveguideportions 104-out-2 and 104-out-3 by distance d2. In some embodiments,distance d2 is greater than 1 micrometer and preferably, greater than orequal to 2 micrometers. In some embodiments, adjacent spiral rounds areseparated by a predetermined distance so that light is not evanescentlycoupled between adjacent spiral rounds. In some embodiments, thepredetermined distance is greater than 1 micrometer and preferably,greater than or equal to 2 micrometers.

In some embodiments, the first plurality of spiral rounds (e.g.,106-in-1 to 106-in-n) has a first number of spiral rounds and the secondplurality of spiral rounds (e.g., 104-in-1 to 104-in-n) has a secondnumber of spiral rounds. In some embodiments, the third plurality ofspiral rounds (e.g., 104-out-1 to 104-out-n) has a third number ofspiral rounds that corresponds to (e.g., equals, is substantially thesame as, differs by no more than 1 spiral round) the second number ofspiral rounds. In some embodiments, the fourth plurality of spiralrounds (e.g., 106-out-1 to 106-out-n) has a fourth number of spiralrounds that corresponds to (e.g., equals, is substantially the same as,differs by no more than 1 spiral round) the first number of spiralrounds.

For example, for an optical delay device that has an optical pathcorresponding to a 5 nanosecond delay, the first number of spiral roundsor the fourth number of spiral rounds is approximately 130. In anotherexample, for an optical delay device that has an optical pathcorresponding to a 10 nanosecond delay, the first number of spiralrounds or the fourth number of spiral rounds is approximately 190.

For example, the second number of spiral rounds or the third number ofspiral rounds is approximately 7 spiral rounds. In some embodiments, thesecond number of spiral rounds or the third number of spiral rounds isindependent of the optical path length L of optical delay device 100.

In some embodiments, optical delay device 100 includes at least 10spiral rounds (e.g., a total number of spiral rounds in the firstplurality of spiral rounds, the second plurality of spiral rounds, thethird plurality of spiral rounds, and the fourth plurality of spiralrounds is at least 10). In some embodiments, optical delay device 100includes at least 100 spiral rounds (e.g., the total number of spiralrounds in the first plurality of spiral rounds, the second plurality ofspiral rounds, the third plurality of spiral rounds, and the fourthplurality of spiral rounds is at least 100). For example, for an opticaldelay device that has an optical path corresponding to a 5 nanoseconddelay, the total number of spiral rounds is approximately 140, theoptical path length L is approximately 40 centimeters, and the opticaldelay device would have lateral dimensions of approximately 1.7millimeters by 1.7 millimeters (e.g., a maximum diameter ofapproximately 0.85 millimeters).

In another example, for an optical delay device that has an optical pathcorresponding to a 10 nanosecond delay, the total number of spiralrounds is approximately 200, the optical path length is approximately 80centimeters, and the optical delay device would have lateral dimensionsof approximately 2.3 millimeters by 2.3 millimeters (e.g., a maximumdiameter of approximately 1.15 millimeters).

In another example, for an optical delay device that has an optical pathlength L that is approximately 160 centimeters, the optical delay devicewould have lateral dimensions of approximately 3.4 millimeters by 3.4millimeters (e.g., a maximum diameter of approximately 1.7 millimeters).

Referring to inset E, which shows a top view of a portion of centerregion 102, first single-mode waveguide 102-A having third width w3 isshown located in center region 102. A first end of first single-modewaveguide 102-A is coupled to waveguide portion 104-in-n, which is aportion of first coupler 104-in, and a second end of first single-modewaveguide 102-A is coupled to waveguide portion 104-out-n, which is aportion of second coupler 104-out. As shown, first single-mode waveguide102-A includes one or more bends. Although only two bends are shown ininset E, first single-mode waveguide 102-A may include any number ofbends.

In some embodiments, as shown, first multi-mode waveguide 106-in, secondmulti-mode waveguide 106-out, first single-mode waveguide 102-A, firstcoupler 104-in, and second coupler 104-out are formed in a same layer ofa material or in a same layer of two or more materials on a substrate189. In some embodiments, first multi-mode waveguide 106-in, secondmulti-mode waveguide 106-out, first single-mode waveguide 102-A, firstcoupler 104-in, and second coupler 104-out have a same height h. In someembodiments, the layer of material has a largely uniform thicknessand/or height.

FIG. 2A illustrates an optical delay device 200 and an optical path oflight propagating through optical delay device 200 in accordance withsome embodiments. Optical delay device 200 includes waveguides (e.g.,first multi-mode waveguide 106-in, second multi-mode waveguide 106-out,and first single-mode waveguide 102-A), couplers (e.g., first coupler104-in and second coupler 104-out), and regions (e.g., center region102, first annular region 104, second annular region 106) describedabove with respect to optical delay device 100 in FIGS. 1A-1C anddetails regarding such features are not repeated here for brevity.

In addition to the waveguides and couplers described with respect tooptical delay device 100, optical delay device 200 also includes aninput coupler 108-in and an output coupler 108-out. Input coupler 108-inis coupled (e.g., physically, optically) to first multi-mode waveguide106-in at the location of input 191 and is configured to receive lightfrom input coupler 108-in and propagate the light toward first coupler104-in. Output coupler 108-out is coupled (e.g., physically, optically)to second multi-mode waveguide 106-out at the location of output 192 andis configured to propagate light received from second coupler 104-outtoward output coupler 108-out.

In some embodiments, optical delay device may also include an inputsingle-mode waveguide 202-in that is coupled to input coupler 108-in atjunction 298 (shown in FIG. 2E). Input single-mode waveguide 202-in isconfigured to receive light and transmit light toward input coupler108-in. In some embodiments, optical delay device may also include anoutput single-mode waveguide 202-out that is coupled to output coupler108-out at junction 299 (shown in FIG. 2E). Output single-mode waveguide202-out is configured to receive light from output coupler 108-out andoutput the light.

Lines with upward pointing arrows correspond to waveguides that spiralinward towards center region 102 (e.g., input single-mode waveguide202-in, input coupler 108-in, first multi-mode waveguide 106-in, andfirst coupler 104-in) and lines with downward pointing arrows correspondto waveguides that spiral outwards from center region 102 (e.g., outputsingle-mode waveguide 202-out, output coupler 108-out, second multi-modewaveguide 106-out, and second coupler 104-out).

FIGS. 2B and 2C are plan views of optical delay device 200 in accordancewith some embodiments. In addition to features described above withrespect to optical delay device 100, optical delay device 200 alsoincludes a third annular region 108 that surrounds second annular region106, which surrounds first annular region 104, which surrounds centerregion 102. At least a portion (e.g., a majority portion, more than 90%)of each of input coupler 108-in and output coupler 108-out are disposedin (e.g., located in) third annular region 108.

In some embodiments, when optical delay device includes inputsingle-mode waveguide 202-in and output single-mode waveguide 202-out,at least a portion of each of input single-mode waveguide 202-in andoutput single-mode waveguide 202-out are disposed in (e.g., located in)third annular region 108.

Optical delay device 200 is configured to receive light 199 at input 291and to propagate light 199 through waveguide portions within thirdannular region 108 toward second annular region 106, through secondannular region 106 toward first annular region 104, through firstannular region 104 toward center region 102, through center region 102toward first annular region 104, through first annular region towardsecond annular region 106, and then through second annular region 106toward third annular region 108, and to output light 199 at output 292.

FIG. 2D shows zoomed-in views of an output region 202 a of optical delaydevice 200 and an input region 202 b of optical delay device 200,respectively, as shown in FIG. 2B, in accordance with some embodiments.As shown, input coupler 108-in includes a portion that has a radius ofcurvature that is substantially the same as (e.g., same, equal to,differing by less than 5%) the first radius of curvature of firstoutmost spiral round 112-1. Input coupler 108-in includes a portion thathas a radius of curvature that is substantially the same as (e.g.,differing by less than 5%) the eighth radius of curvature of fourthoutmost spiral round 112-8. Input coupler 108-in and output coupler108-out each include at least a portion of a spiral round. In someembodiments, input coupler 108-in may include a fifth plurality ofspiral rounds and output coupler 108-out may include a sixth pluralityof spiral rounds.

FIG. 2E is a linearized (or stretched-out) view of optical delay device200 shown in FIG. 2B, illustrating the dimensions of various portions ofoptical delay device 200. As shown in FIG. 2E, optical delay device 200provides an optical path having an overall length A for light 199propagating through:

-   -   input coupler 108-in;    -   first multi-mode waveguide 106-in;    -   first coupler 104-in;    -   first single-mode waveguide 102-A;    -   second coupler 104-out;    -   second multi-mode waveguide 106-out; and    -   output coupler 108-out.

In some embodiments, when optical delay device 200 includes inputsingle-mode waveguide 202-in and output single-mode waveguide 202-out,the optical path of light 199 also includes:

-   -   input single-mode waveguide 202-in; and    -   output single-mode waveguide 202-out.

As shown in FIG. 2E, input coupler 108-in has a sixth length L6 andoutput coupler 108-out has a seventh length L7. In some embodiments,sixth length L6 and seventh length L7 are each larger than third lengthL3 of first single-mode waveguide 102-A (i.e., L3<<L6, L7). In someembodiments, sixth length L6 and seventh length L7 are substantially thesame (e.g., differing by less than 1% or 0.1%). In some embodiments,sixth length L6 and seventh length L7 are each greater than 1 millimeter(e.g., L6, L7>1 millimeter). In some embodiments, sixth length L6 andseventh length L7 are approximately 3 millimeters (e.g., L6, L7˜3millimeters). In some embodiments, when input single-mode waveguide102-in and output single-mode waveguide 102-out are included in opticaldelay device 200, the length of input single-mode waveguide 202-inbetween input 291 and the input coupler 108-in is about equal to thelength of output single-mode waveguide 202-out between output 292 andthe output coupler 108-out. In some embodiments, each of the length ofinput single-mode waveguide 202-in and the length of output single-modewaveguide 202-out is less than the length of an outmost spiral round(e.g., each length is less than three quarters of an outmost spiralround). Alternatively, in some embodiments, input single-mode waveguide102-in and output single-mode waveguide 102-out are not included inoptical delay device 200.

In some embodiments, input coupler 108-in includes at least a portion ofa spiral turn. In some embodiments, output coupler 108-out includes atleast a portion of a spiral turn.

In some embodiments, when optical delay device 200 includes inputsingle-mode waveguide 202-in and output single-mode waveguide 202-out,input single-mode waveguide 202-in has an eighth width w8 and outputsingle-mode waveguide 202-out has a ninth width w9. Each of eighth widthw8 and a ninth width w9 is smaller than each of the first width w1 offirst multi-mode waveguide 106-in and the second width w2 of secondmulti-mode waveguide 106-out (i.e., w8, w9<w1, w2). In some embodiments,eighth width w8 and a ninth width w9 are the substantially the same(e.g., differing by less than 5%). In some embodiments, one or more ofeighth width w8 and a ninth width w9 is equal to third width w3 of firstsingle-mode waveguide 102-A (e.g., w8, w9˜w1). In some embodiments,eighth width w8 and a ninth width w9 are between 400 nanometers and 500nanometers (e.g., 400 nanometers≤w8, w9≤500 nanometers). In someembodiments, eighth width w8 and a ninth width w9 are less than 1micrometer (e.g., w8, w9≤1 micrometer).

Input coupler 108-in has a width that tapers from first width w1 toeighth width w8. Output coupler 108-out has a width that tapers fromsecond width w2 to ninth width w9.

Input coupler 108-in is configured to adiabatically couple light frominput single-mode waveguide 202-in to first multi-mode waveguide 106-in.Output coupler 108-out is configured to adiabatically couple light fromsecond multi-mode waveguide 106-out to fourth single-mode waveguide202-out. For example, one or more of input coupler 108-in and outputcoupler 108-out may have a linear taper profile, a parabolic taperprofile, or an exponential taper profile. In some cases, a largesttapering angle θ of input coupler 108-in and output coupler 108-out isless than 0.3 degrees.

FIGS. 3A-3C are flowcharts illustrating a method of propagating light tocreate an optical delay in accordance with some embodiments.

The method 300 includes (310) receiving light and (312) propagating thelight (e.g., light 199) along an input single-mode waveguide 202-intoward an input coupler 108-in and propagating the light along the inputcoupler toward a first multi-mode waveguide 106-in. In some embodiments,the method 300 also includes (312-1) propagating the light along a pathhaving a first radius of curvature.

The method 300 also includes (320) propagating the light in the firstmulti-mode waveguide 106-in toward a first coupler 104-in andpropagating the light in the first coupler 104-in toward a firstsingle-mode waveguide 102-A. The first multi-mode waveguide 106-in andthe first coupler 104-in provide a first light path that spirals inwardtoward a center region 102. The first single-mode waveguide 102-A isdisposed in the center region 102.

In some embodiments, (322 shown in FIG. 3B) the first light pathincludes a first plurality of spiral rounds (e.g., spiral rounds106-in-1 to 106-in-n) corresponding to the first multi-mode waveguide106-in and a second plurality of spiral rounds (e.g., spiral rounds104-in-1 to 104-in-n) corresponding to the first coupler 104-in. Thefirst plurality of spiral rounds includes a first outmost spiral portion112-1 that has a first radius of curvature and a first inmost spiralportion 112-2 that has a second radius of curvature that is smaller thanthe first radius of curvature. Spiral portions between the first outmostspiral portion and the first inmost spiral portion have successivelydecreasing radii that decreases continuously and monotonously betweenthe first radius of curvature and the second radius of curvature. Thesecond plurality of spiral rounds includes a second outmost spiralportion 112-3 that has a third radius of curvature that is smaller thanthe second radius of curvature. The second plurality of spiral roundsalso includes a second inmost spiral portion 112-4 that has a fourthradius of curvature that is smaller than the third radius of curvature.Spiral portions between the second outmost spiral portion and the secondinmost spiral portion have successively decreasing radii that decreasescontinuously and monotonously between the third radius of curvature andthe fourth radius of curvature.

In some embodiments, (322-1) the first plurality of spiral rounds has afirst number of spiral rounds and the second plurality of spiral roundshas a second number of spiral rounds. In some embodiments, the firstnumber of spiral rounds is substantially the same as (e.g., notdiffering by more than one spiral round) the second number of spiralrounds. In some embodiments, one or more of the first number of spiralrounds and the second number of spiral rounds is more than 100.

In some embodiments, (322-2) the third radius of curvature issubstantially equal to (e.g., differing by less than 5%) the secondradius of curvature.

In some embodiments, (324) propagating the light along the first lightpath includes propagating the light along the first multi-mode waveguide106-in without evanescently coupling the light into the secondmulti-mode waveguide 106-out and propagating the light along the firstcoupler 104-in without evanescently coupling the light into the secondcoupler 104-out.

The method 300 also includes (330 shown FIG. 3A) propagating light alongthe first single-mode waveguide 102-A toward a second coupler 104-out.In some embodiments, the method 300 also includes (332) propagating thelight along a curved path having a radius of curvature that is smallerthan each of a fourth radius of curvature and a fifth radius ofcurvature.

The method 300 also includes (340) propagating the light in the secondcoupler 104-out toward a second multi-mode waveguide 106-out andpropagating the light in the second multi-mode waveguide 106-out. Thesecond coupler 104-out and the second multi-mode waveguide 106-outprovide a second light path that spirals outward from the center region102.

In some embodiments, (342) the second light path includes a thirdplurality of spiral rounds (e.g., 104-out-1 to 104-out-n) correspondingto the second coupler 104-out and a fourth plurality of spiral rounds(e.g., 106-out-1 to 106-out-n) corresponding to the second multi-modewaveguide 106-out. The third plurality of spiral rounds includes a thirdinmost spiral portion 112-5 that has a fifth radius of curvature and athird outmost spiral portion 112-6 that has a sixth radius of curvaturethat is larger than the fifth radius of curvature. Spiral portionsbetween the third inmost spiral portion and the third outmost spiralportion have successively increasing radii that increases continuouslyand monotonously between the fifth radius of curvature and the sixthradius of curvature. The fourth plurality of spiral rounds includes afourth inmost spiral portion 112-7 that has a seventh radius ofcurvature that is smaller than the sixth radius of curvature. The fourthplurality of spiral rounds also includes a fourth outmost spiral portion112-8 that has an eighth radius of curvature that is larger than theseventh radius of curvature. Spiral portions between the fourth inmostspiral portion and the fourth outmost spiral portion have successivelyincreasing radii that increases continuously and monotonously betweenthe seventh radius of curvature and the eighth radius of curvature. Insome embodiments, (342-1) the third plurality of spiral rounds has athird number of spiral rounds that corresponds to (e.g., equals to,differs by less than 2 spiral rounds) the second number of spiral roundsand the fourth plurality of spiral rounds has a fourth number of spiralrounds that corresponds (e.g., equals to, differs by less than 2 spiralrounds) to the first number of spiral rounds. In some embodiments,(342-2) the eighth radius of curvature is substantially equal to (e.g.,differing by less than 5%) the first radius of curvature, the seventhradius of curvature is substantially equal to (e.g., differing less than5%) the second radius of curvature, the sixth radius of curvature issubstantially equal to (e.g., differing by less than 5%) the thirdradius of curvature, and the fifth radius of curvature is substantiallyequal to (e.g., differing by less than 5%) the fourth radius ofcurvature. In some embodiments, (344) propagating light along the secondlight path includes propagating the light along the second coupler104-out without evanescently coupling the light into the first coupler104-in and propagating the light along the second multi-mode waveguide106-out without evanescently coupling the light into the firstmulti-mode waveguide 106-in.

The method 300 also includes (350) outputting the light. In someembodiments, the method also includes (352) coupling the light from thesecond multi-mode waveguide 106-out, through an output coupler 108-out,to an output single-mode waveguide 202-out and propagating the lightalong the output single-mode waveguide 202-out. In some embodiments, themethod 300 also include (352-1) propagating the light along a pathhaving an eighth radius of curvature.

The terminology used in the description of the various describedembodiments herein is for the purpose of describing particularembodiments only and is not intended to be limiting. As used in thedescription of the various described embodiments and the appendedclaims, the singular forms “a”, “an” and “the” are intended to includethe plural forms as well, unless the context clearly indicatesotherwise. It will also be understood that the term “and/or” as usedherein refers to and encompasses any and all possible combinations ofone or more of the associated listed items. It will be furtherunderstood that the terms “includes,” “including,” “comprises,” and/or“comprising,” when used in this specification, specify the presence ofstated features, integers, steps, operations, elements, and/orcomponents, but do not preclude the presence or addition of one or moreother features, integers, steps, operations, elements, components,and/or groups thereof.

As used herein, the term “if” is, optionally, construed to mean “when”or “upon” or “in response to determining” or “in response to detecting”or “in accordance with a determination that,” depending on the context.

The foregoing description, for purpose of explanation, has beendescribed with reference to specific embodiments. However, theillustrative discussions above are not intended to be exhaustive or tolimit the scope of the claims to the precise forms disclosed. Manymodifications and variations are possible in view of the aboveteachings. For example, although FIGS. 1A-1G illustrate an optical delaydevice that includes a first multi-mode waveguide, a second multi-modewaveguide, a first single-mode waveguide, a first coupler, and a secondcoupler, additional waveguides can be added to increase the numberspiral rounds, such as described above with respect to FIGS. 2A-2E. Insome embodiments, fewer components may be used. For example, inaccordance with some embodiments, an optical device includes a firstmulti-mode waveguide; a first optical coupler coupled to the firstmulti-mode waveguide, the first coupler being tapered and curved; and afirst single-mode waveguide having a first end coupled to the firstoptical coupler. Such device may be used in an optical delay device orother optical devices. The embodiments were chosen in order to bestexplain the principles underlying the claims and their practicalapplications, to thereby enable others skilled in the art to best usethe embodiments with various modifications as are suited to theparticular uses contemplated.

What is claimed is:
 1. An optical device, comprising: a first multi-modewaveguide, wherein the first multi-mode waveguide includes a firstplurality of spiral rounds; a first optical coupler coupled to the firstmulti-mode waveguide, the first optical coupler being tapered andcurved; and a first single-mode waveguide having a first end coupled tothe first optical coupler, wherein a first portion of the firstsingle-mode waveguide has a first single-mode radius of curvature havinga first center, a second portion of the first single-mode waveguide hasa second single-mode radius of curvature having a second center, and atleast a portion of the first single-mode waveguide is located betweenthe first center and the second center.
 2. The optical device of claim1, wherein: the optical device is an optical delay device.
 3. Theoptical device of claim 1, wherein: the first multi-mode waveguide has afirst width; the first single-mode waveguide has a second width smallerthan the first width; and a width of the first optical coupler tapersfrom the first width to the second width.
 4. The optical device of claim3 further comprising: a second multi-mode waveguide distinct andseparate from the first multi-mode waveguide; and a second opticalcoupler coupled with the second multi-mode waveguide and a second end,opposite to the first end, of the first single-mode waveguide, thesecond optical coupler being tapered and curved.
 5. The optical deviceof claim 4, wherein: the second multi-mode waveguide has a third widthgreater than the second width; and a width of the second optical couplertapers from the second width to the third width.
 6. The optical deviceof claim 1, further comprising: a second single-mode waveguide; and athird optical coupler having a first end coupled to the secondsingle-mode waveguide and a second end coupled to a first end of thefirst multi-mode waveguide, wherein the first optical coupler is coupledto a second end, opposite to the first end, of the first multi-modewaveguide.
 7. The optical device of claim 6, wherein: the firstmulti-mode waveguide has a first width; the second single-mode waveguidehas a fourth width smaller than the first width; and a width of thethird optical coupler tapers from the fourth width to the first width.8. The optical device of claim 1, wherein the first multi-modewaveguide, the first single-mode waveguide, and the first opticalcoupler are formed in a same planar layer of a material on a substrate.9. The optical device of claim 1, wherein: the first multi-modewaveguide and the first optical coupler spiral inward toward a centerregion of the optical device.
 10. The optical device of claim 1,wherein: the first plurality of spiral rounds includes a first outmostspiral portion having a first radius of curvature and a first inmostspiral portion having a second radius of curvature smaller than thefirst radius of curvature, and spiral portions between the first outmostspiral portion and the first inmost spiral portion and havingsuccessively decreasing radii from the first radius of curvature to thesecond radius of curvature; and the first optical coupler includes asecond plurality of spiral rounds, the second plurality of spiral roundsincluding a second outmost spiral portion having a third radius ofcurvature and a second inmost spiral portion having a fourth radius ofcurvature smaller than the third radius of curvature, and spiralportions between the second outmost spiral portion and the second inmostspiral portion and having successively decreasing radii from the thirdradius of curvature to the fourth radius of curvature.
 11. The opticaldevice of claim 10, wherein the first single-mode waveguide includes acurved portion having a radius of curvature smaller than each of thefourth radius of curvature.
 12. A method, comprising: receiving light;propagating the light in a first multi-mode waveguide toward a firstoptical coupler wherein the first multi-mode waveguide includes a firstplurality of spiral rounds; propagating the light in the first opticalcoupler toward a first single-mode waveguide, the first optical couplerbeing tapered and curved; and propagating the light along the firstsingle-mode waveguide, wherein a first portion of the first single-modewaveguide has a first single-mode radius of curvature having a firstcenter, a second portion of the first single-mode waveguide has a secondsingle-mode radius of curvature having a second center, and at least aportion of the first single-mode waveguide is located between the firstcenter and the second center.
 13. The method of claim 12, wherein: thefirst plurality of spiral rounds includes a first outmost spiral portionhaving a first radius of curvature and a first inmost spiral portionhaving a second radius of curvature smaller than the first radius ofcurvature, and spiral portions between the first outmost spiral portionand the first inmost spiral portion and having successively decreasingradii from the first radius of curvature to the second radius ofcurvature; and the first optical coupler includes a second plurality ofspiral rounds, the second plurality of spiral rounds including a secondoutmost spiral portion having a third radius of curvature and a secondinmost spiral portion having a fourth radius of curvature smaller thanthe third radius of curvature, and spiral portions between the secondoutmost spiral portion and the second inmost spiral portion and havingsuccessively decreasing radii from the third radius of curvature to thefourth radius of curvature.
 14. The method of claim 13, wherein thefirst single-mode waveguide includes a curved portion having a radius ofcurvature smaller than the fourth radius of curvature.
 15. The method ofclaim 12, wherein: the first multi-mode waveguide has a first width; thefirst single-mode waveguide has a second width smaller than the firstwidth; and a width of the first optical coupler tapers from the firstwidth to the second width.
 16. The method of claim 15, furthercomprising: propagating the light from the first single-mode waveguidetoward a second optical coupler coupled with a second end of the firstsingle-mode waveguide opposite to a first end of the first single-modewaveguide coupled to the first optical coupler, the second opticalcoupler being tapered and curved; propagating the light in the secondoptical coupler toward a second multi-mode waveguide distinct andseparate from the first multi-mode waveguide; and propagating the lightalong the second multi-mode waveguide.
 17. The method of claim 16,wherein: the second multi-mode waveguide has a third width greater thanthe second width; and a width of the second optical coupler tapers fromthe second width to the third width.
 18. The optical device of claim 4,wherein: the first plurality of spiral rounds spirals toward the firstoptical coupler in a direction that is one of: a clockwise direction ora counterclockwise direction; and the second multi-mode waveguideincludes a second plurality of spiral rounds that spirals away from thesecond optical coupler in a direction that is the other of: theclockwise direction or the counterclockwise direction.
 19. An opticaldevice, comprising: a first multi-mode waveguide, wherein the firstmulti-mode waveguide includes a first plurality of spiral rounds; afirst optical coupler coupled to the first multi-mode waveguide, thefirst optical coupler being tapered and curved; and a first single-modewaveguide having a first end coupled to the first optical coupler,wherein a first portion of the first single-mode waveguide curves in adirection that is one of a clockwise direction and a counterclockwisedirection and a second portion of the first single-mode waveguide curvesin a direction that is the other of the clockwise direction and thecounterclockwise direction.